matrix of a linear transformation

• Oct 18th 2009, 05:29 PM
noles2188
matrix of a linear transformation
Consider the polynomials f(t) = t + 1 and g(t) = (t + 2)(t + k), where k is an arbitrary constant. For which values of the constant k are the three polynomials f(t), tf(t) and g(t) a basis of P2?
• Oct 18th 2009, 05:46 PM
Bruno J.
This will happen when the matrix of coefficients

$\left(
\begin{array}{lll}
1 & 0 & 2 k \\
1 & 1 & k+2 \\
0 & 1 & 1
\end{array}
\right)$

is nonsingular. Evaluate its determinant, and find the values of $k$ for which it is nonzero.